Physics - Modern Physics Question with Solution | TestHub

In a hydrogen like atom, when an electron makes an transition from an energy level with $n$ to $n-1$, the frequency of emitted radiation is $v=Rc{Z}^2\left[\frac{1}{(n-1{)}^2}-\frac{1}{n^2}\right]=\frac{Rc{Z}^2(2n-1)}{n^2(n-1{)}^2}$ As $n>>1$ $\therefore \mathrm{v}=\frac{Rc{Z}^{2}2n}{n^4}=\frac{2Rc{Z}^2}{n^3}$ or $v\propto \frac{1}{n^3}$